Answer:
[tex]\dfrac{dx}{dt}= kx[6000-x], x(0)=0, k>0[/tex]
Step-by-step explanation:
Total Number of Students =6000
Number of students who have contracted the flu =x(t)
Number of students who have not contracted the flu =6000- x(t)
Now, the rate at which the disease spreads is proportional to the number of interactions between students with the flu and students who have not yet contracted it.
[tex]\dfrac{dx(t)}{dt}\propto x(t)[6000-x(t)] \\$Introducing the constant of proportionality, k, we have:\\\dfrac{dx}{dt}= kx[6000-x][/tex]
Initially, the campus is uninfected, therefore: x(0)=0
Therefore, a differential equation governing the number of students x(t) who have contracted the flu is:
[tex]\dfrac{dx}{dt}= kx[6000-x], x(0)=0, k>0[/tex]
